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a radio transmission tower is 241 feet tall. a guy wire is to be attached 6 feet from the top and is to make an angle of 24 degrees with the ground. how many feet long should the guy wire be?

User Anil Shah
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1 Answer

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Final answer:

To find the length of the guy wire, you can use trigonometry.

Step-by-step explanation:

To calculate the length of the guy wire, we can use trigonometry. The guy wire forms a right triangle with the height of the tower and the distance from the top of the tower to the point where the wire is attached. The angle made by the guy wire with the ground is given as 24 degrees.

We can use the sine function to find the length of the guy wire. The sine of an angle is equal to the length of the side opposite the angle divided by the hypotenuse. In this case, the opposite side is the height of the tower minus the distance from the top to the attachment point, and the hypotenuse is the length of the guy wire.

So, the length of the guy wire can be found using the equation: sin(24 degrees) = (241 ft - 6 ft) / x, where x is the length of the guy wire. Solving for x, we have: x = (241 ft - 6 ft) / sin(24 degrees).

Plugging in the values, we get: x = 235 ft / sin(24 degrees). Using a calculator, we find that sin(24 degrees) is approximately 0.4067. Therefore, the length of the guy wire should be approximately 577.2 feet.

User Joe Koberg
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